psfun_z_quadrature_mod

This module computes the matrix-function vector product by means of the approximation of $f(A)\mathbf{x}$ based on quadrature formula, i.e., having computed the poles and the scalings of the formula solves $N$ linear systems to approximate the product.

Uses

- psfun_base_quadrature_mod
- psb_base_mod
- psfun_utils_mod
- ogpf
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Used by

- Descendants:
- psfun_z_quadrules_mod
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Nodes of different colours represent the following:

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Interfaces

hhtmethod1

Abstract Interfaces

zquadfun zquadrule

Derived Types

psfun_z_quadrature

Subroutines

psfun_z_computepoles psfun_z_quadratureplot psfun_z_setmatrix psfun_z_setpreconditioner

Interfaces

public interface hhtmethod1

Method 1 of Hale, Nicholas; Higham, Nicholas J.; Trefethen, Lloyd N. Computing $\mathbf{A}^\alpha,\ \log(\mathbf{A})$ , and related matrix functions by contour integrals. SIAM J. Numer. Anal. 46 (2008), no. 5, 2505--2523.

public subroutine hhtmethod1(zfun, xi, c, eta, sign, N, info, cparams, rparams)

Arguments

Type	Intent	Optional	Attributes		Name
procedure(zquadfun),	intent(in),		pointer	::	zfun	Function to integrate
complex(kind=psb_dpk_),	intent(out),		allocatable, dimension(:)	::	xi	Poles of the formula
complex(kind=psb_dpk_),	intent(out),		allocatable, dimension(:)	::	c	Scaling of the formula
real(kind=psb_dpk_),	intent(out)			::	eta	Global Scaling
real(kind=psb_dpk_),	intent(out)			::	sign	Sign for A
integer(kind=psb_ipk_),	intent(in)			::	N	Number of Poles
integer(kind=psb_ipk_),	intent(out)			::	info	Flag on the results
complex(kind=psb_dpk_),	intent(in),	optional	dimension(:)	::	cparams	Optional complex parameters
real(kind=psb_dpk_),	intent(in),	optional	dimension(:)	::	rparams	Optional real parameters

Abstract Interfaces

abstract interface

public function zquadfun(z) result(res)

Arguments

Type Intent Optional Attributes Name

complex(kind=psb_dpk_), intent(in) :: z

Return Value complex(kind=psb_dpk_)

Type	Intent	Optional	Attributes		Name
complex(kind=psb_dpk_),	intent(in)			::	z

abstract interface

public subroutine zquadrule(zfun, xi, c, eta, sign, N, info, cparams, rparams)

To integrate a function that take as inputs complex number and gives as output complex numbers

Arguments

Type	Intent	Optional	Attributes		Name
procedure(zquadfun),	intent(in),		pointer	::	zfun	Function to integrate
complex(kind=psb_dpk_),	intent(out),		allocatable, dimension(:)	::	xi	Poles of the formula
complex(kind=psb_dpk_),	intent(out),		allocatable, dimension(:)	::	c	Scaling of the formula
real(kind=psb_dpk_),	intent(out)			::	eta	Global Scaling
real(kind=psb_dpk_),	intent(out)			::	sign	Sign for A
integer(kind=psb_ipk_),	intent(in)			::	N	Number of Poles
integer(kind=psb_ipk_),	intent(out)			::	info	Flag on the results
complex(kind=psb_dpk_),	intent(in),	optional	dimension(:)	::	cparams	Optional complex parameters
real(kind=psb_dpk_),	intent(in),	optional	dimension(:)	::	rparams	Optional real parameters

Derived Types

type, public, extends(psfun_quadrature) :: psfun_z_quadrature

Components

Type	Visibility	Attributes		Name
type(psb_dspmat_type),	public,	pointer	::	a	Matrix on which we work
complex(kind=psb_dpk_),	public,	allocatable, dimension(:)	::	c	Scaling of the formula
type(psb_desc_type),	public		::	desc_a	Descriptor for parallel environment
real(kind=psb_dpk_),	public		::	eta	Global Scaling
type(psb_dprec_type),	public,	pointer	::	prec	Preconditioner for the solution of the associate linear systems
real(kind=psb_dpk_),	public		::	sign	Sign for $A$
complex(kind=psb_dpk_),	public,	allocatable, dimension(:)	::	xi	Poles of the formula

Type-Bound Procedures

procedure, public, pass(quad) :: computepoles => psfun_z_computepoles
procedure, public, pass(quad) :: plot => psfun_z_quadratureplot
generic, public :: set => setmatrix, setpreconditioner
procedure, public, pass(quad) :: setmatrix => psfun_z_setmatrix
procedure, public, pass(quad) :: setpreconditioner => psfun_z_setpreconditioner

Subroutines

public subroutine psfun_z_computepoles(quad, quadformula, zfun, N, info, cparams, rparams)

Compute the poles for a given combination of quadrature rule and quadrature formula

Arguments

Type	Intent	Optional	Attributes		Name
class(psfun_z_quadrature),	intent(inout)			::	quad	Quadrature type
procedure(zquadrule),	intent(in),		pointer	::	quadformula	Quadrature formula
procedure(zquadfun),	intent(in),		pointer	::	zfun	Function to integrate
integer(kind=psb_ipk_),	intent(in)			::	N	Number of poles
integer(kind=psb_ipk_),	intent(out)			::	info	Flag on the results
complex(kind=psb_dpk_),	intent(in),	optional	dimension(:)	::	cparams	Optional complex parameters
real(kind=psb_dpk_),	intent(in),	optional	dimension(:)	::	rparams	Optional real parameters

public subroutine psfun_z_quadratureplot(quad, zfun, info, filename)

Plots on the complex plane the quadrature poles, and plots the weights of the formula

Arguments

Type	Intent	Optional	Attributes		Name
class(psfun_z_quadrature),	intent(in)			::	quad	Quadrature rule
procedure(zquadfun),	intent(in),		pointer	::	zfun	Function to integrate
integer(kind=psb_ipk_),	intent(out)			::	info
character(len=*),	intent(in),	optional		::	filename

public subroutine psfun_z_setmatrix(quad, a)

Set the matrix $A$ for $f(A)x$

Arguments

Type	Intent	Optional	Attributes		Name
class(psfun_z_quadrature),	intent(inout)			::	quad	Quadrature type
type(psb_dspmat_type),			target	::	a	Matrix on which we work

public subroutine psfun_z_setpreconditioner(quad, prec)

Set the preconditioner to use for the given quadrature formula

Arguments

Type	Intent	Optional	Attributes		Name
class(psfun_z_quadrature),	intent(inout)			::	quad	Quadrature type
type(psb_dprec_type),			target	::	prec	Preconditioner for the solution of the associate linear systems

psfun_z_quadrature_mod Module

Contents

Interfaces

Abstract Interfaces

Derived Types

Subroutines

Uses

Used by

Descendants:

Contents

Interfaces

Abstract Interfaces

Derived Types

Subroutines

Interfaces

public interface hhtmethod1

public subroutine hhtmethod1(zfun, xi, c, eta, sign, N, info, cparams, rparams)

Arguments

Abstract Interfaces

abstract interface

public function zquadfun(z) result(res)

Arguments

Return Value complex(kind=psb_dpk_)

abstract interface

public subroutine zquadrule(zfun, xi, c, eta, sign, N, info, cparams, rparams)

Arguments

Derived Types

type, public, extends(psfun_quadrature) :: psfun_z_quadrature

Components

Type-Bound Procedures

Subroutines

public subroutine psfun_z_computepoles(quad, quadformula, zfun, N, info, cparams, rparams)

Arguments

public subroutine psfun_z_quadratureplot(quad, zfun, info, filename)

Arguments

public subroutine psfun_z_setmatrix(quad, a)

Arguments

public subroutine psfun_z_setpreconditioner(quad, prec)

Arguments